Question

a paper clip is shown on the graph. the distance from a to b represents the length of the paper clip. dilate the paper clip by a scale factor of 2 with the center of dilation at the origin. point a is 3 cm up from point b, so point a is 6 cm up from point b. what are the coordinates of point a?

Explanation:

Step1: Find the coordinates of point A

From the graph, point A has coordinates \((4,3)\).

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\) where \(k = 2\) (scale factor).
For \(x\)-coordinate: \(x'=2\times4 = 8\)
For \(y\)-coordinate: \(y'=2\times3=6\)

Answer:

\((8,6)\)